One pion production in neutrino–nucleon scattering and the different parameterizations of the weak N→ΔN→Δ vertex

The N→ΔN→Δ weak vertex provides an important contribution to the one pion production in neutrino–nucleon and neutrino–nucleus scattering for πN   invariant masses below 1.4 GeV. Beyond its interest as a tool in neutrino detection and their background analyses, one pion production in neutrino–nucleon scattering is useful to test predictions based on the quark model and other internal symmetries of strong interactions. Here we try to establish a connection between two commonly used parameterizations of the weak N→ΔN→Δ vertex and form factors (FF) and we study their effects on the determination of the axial coupling C5A(0), the common normalization of the axial FF, which is predicted to hold 1.2 by using the PCAC hypothesis. Predictions for the νμp→μ−pπ+νμp→μ−pπ+ total cross sections within the two approaches, which include the resonant Δ++Δ++ and other background contributions in a coherent way, are compared to experimental data.